Finite Group Databasebeta

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C2×C17×(C43⋊C3)⋊C7 #44502014

order30702
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C17 · Schur multiplier (H2) = C1

Aliases

direct productC2×C17×(C43⋊C3)⋊C7
unambiguous semidirect product(C2×C43⋊C3)⋊(C7×C17)
unambiguous semidirect product(C2×C43⋊C7)⋊(C3×C17)
unambiguous semidirect product(C2×C17×C43⋊C3)⋊C7
unambiguous semidirect product(C2×C17×C43⋊C7)⋊C3

Splittings

Fitting, socle, HallC2×C17×C43 ⋊ C3×C7
derived, SylowC43 ⋊ C2×C3×C7×C17
HallC2×C17×C43⋊C7 ⋊ C3
HallC17×C43⋊C7 ⋊ C2×C3
HallC2×C17×C43⋊C3 ⋊ C7
HallC17×C43⋊C3 ⋊ C2×C7
HallC17×C43 ⋊ C2×C3×C7
HallC2×C43⋊C7 ⋊ C3×C17
HallC43⋊C7 ⋊ C2×C3×C17
HallC2×C43⋊C3 ⋊ C7×C17
HallC43⋊C3 ⋊ C2×C7×C17
HallC2×C43 ⋊ C3×C7×C17

Subgroups

subgroupG/H
center, hypercenterC2×C17(C43⋊C3)⋊C7
commutator, cosocle, hypocenterC43C2×C3×C7×C17
FrattiniC1G
Fitting, socleC2×C17×C43C3×C7
LCSG ▷ C43
UCSC1 ◁ C2×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1462

Conjugacy classes & character table

782 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30702, 7);